This website (link to bookmark: http://www.pawelpilarczyk.com/quadr/) contains software and data relatd to two papers:

- [1]
*Rigorous numerics for the quadratic family*by A. Golmakani, C. E. Koudjinan, S. Luzzatto, and P. Pilarczyk - [2]
*Rigorous computation of escape times for parameter intervals in the quadratic map*by P. Pilarczyk and S. Luzzatto

**Files for download related to the paper [1]:**

- progcode1.zip – the source code of the program, published here under the terms of the GNU General Public License, version 3
- phpcode.zip – the source code of the website (programmed in PHP), published here under the terms of the GNU Affero General Public License, version 3
- computation_log.zip (91 MB) – the original computation log produced by the program, which is a basis for the results discussed in the paper and for the figures contained therein (227MB after unzipping)

**Files for download related to the paper [2]** (see note below on the data contained in the archive files):

- progcode2.zip – the source code of the program, published here under the terms of the GNU General Public License, version 3
- noChoppingTest.zip (39 MB) – computations used in Section 2 to analyze the iterated intervals at first encounter with Δ
- w10data.zip (31 MB) – data from computations for six intervals: [1.4,1.5], …, [1.9,2.0] (used for Figure 6)
- w4data.zip (0.7 MB)
– complete computation with
*w*=10^{−4}(for Figures in Section 3) - w5data.zip (5 MB)
– complete computation with
*w*=10^{−5}(for Figures in Section 3) - w6data.zip (41 MB)
– complete computation with
*w*=10^{−6}(for Figures in Section 3) - w7data.zip (273 MB)
– complete computation with
*w*=10^{−7}(for Figures in Section 3) - w8data_15-30.zip (453 MB)
– complete computation with
*w*=10^{−8}and*N*_{0}=15,…,30 (for Figures in Section 3) - w8data_31-35.zip (588 MB)
– complete computation with
*w*=10^{−8}and*N*_{0}=31,…,35 (for Figures in Section 3) - w8data_36-40.zip (620 MB)
– complete computation with
*w*=10^{−8}and*N*_{0}=36,…,40 (for Figures in Section 3) - bisectionTest.zip (0.1 MB) – computations used in Section 4 to check the effect of the number of bisection steps on the results

**Description of the CSV files.**
Each CSV file name contains a capital letter indicating the type of data:

**G**(files "*G.csv") – "good" intervals, that is, intervals satisfying the escape condition (case P1a in [1], pg. 12),**A**(files "*A.csv") – intervals abandoned due to reaching the limit of iterations (case P3 in [1], pg. 13),**C**and**F**(files "*C.csv" and "*F.csv") – intervals with a mismatch in the sign of the derivative of*c*_{n}or*f*^{n}, respectively (case P2a in [1], pg. 13),**D**(files "*D.csv") – cases of intervals hitting Δ but at an iterate*N*<*N*_{0}or not satisfying the escape condition (case P1b in [1], pg. 12).

- the
**G**files: the actual number*N*of iterates, a lower bound on the width of the iterated interval ω_{N}, a lower bound on the left endpoint of the interval ω, an upper bound on the right endpoint of the interval ω, a lower bound on the width of the interval ω; for example:

22 2.20444158646 1.88489967547 1.88498738876 8.77132775368e-5 - the
**A**files: the actual number*N*of the iterate at which an interval ω was abandoned, a lower bound on the left endpoint of the interval ω, an upper bound on the width of the interval ω; for example:

100 1.75700000000 1.00000000001e-3 - the
**C**and**F**files: the actual number*N*of the iterate at which the problem with an interval ω was encountered, the left endpoint of the interval ω rounded to the nearest, for example:

24 1.48300000000 - the
**D**files: the actual number*N*of the iterate at which the interval ω_{N}hit Δ, the left endpoint of the interval ω rounded to the nearest, a lower bound on the width of the interval ω_{N}; for example:

39 1.41500000000 3.99738138690e-1

An interface is provided to running the program introduced in the paper [1]. Since some computations can be very lengthy and memory-consuming, there are some limits set up on what one can do using this interface. Please, download and compile the program to run it at your computer in order to use full capabilities of the software.

Please, fill out the form with desired values of parameters,
and click the RUN button to see the result under the form.
Then you are welcome to adjust some parameters,
and run the computation again.

*Please, note that in the short version of the form, there are only
a few selected parameters shown below (thus the numbering is not
contiguous). Click the button below to toggle between the short list
and the long one.*

[After you hit the RUN button to run the program, the results of the computation will be displayed here after the computation has been completed.]